Liability insurance includes both public and employer’s liability insurance. Public liability insurance isn’t just for injury or damage to persons directly, it can also include damage to property and caused loss of earnings: in fact it basically covers you for liability where you have caused any kind of negative effect to a person or company. This includes affect on people’s health and of course injuries and death both directly and indirectly caused by you or your business and its employees. Even if your employee is responsible, liability may well still fall to you: and don’t assume having given adequate training to a staff that ignored it will stop you being liable. If you are a company especially the corporate entity may be responsible, and without insurance potentially ruined. Public liability insurance will also cover you and your business where damage has been done to property: it can even include intentional damage by your employees and even theft by employees working for you: this can be extended to sub contractors upon request.
Employer’s liability insurance basically covers your employees, mainly this includes their health including injuries and death where you or your business are liable in whole or part. It may be that they missed out on a vital bit of training you should have given or had not been given adequate equipment for a job, such as the wrong type of ladder. There is a good chance that an employee will sue you and win, or it could be their family if the worst has happened; the only way to protect your business is to have adequate insurance that will cover you in a civil action, though of course not if you are presented with a criminal charge.